Far-infrared spectroscopy of nanoscopic InAs rings

Abstract

We have employed time-dependent local-spin-density theory to analyze the far-infrared transmission spectrum of InAs self-assembled nanoscopic rings recently reported ͓A. Lorke et al., Phys. Rev. Lett. ͑to be published͔͒. The overall agreement between theory and experiment is fairly good, which on the one hand confirms that the experimental peaks indeed reflect the ringlike structure of the sample, and on the other hand, asseses the suitability of the theoretical method to describe such nanostructures. The addition energies of oneand two-electron rings are also reported and compared with the corresponding capacitance spectra. Recent progress in nanofabrication techniques1,2 has allowed us to construct self-assembled nanoscopic InGaAs quantum rings occupied with one or two electrons each, and submitted to perpendicular magnetic fields ͑B͒ of up to 12 T. These are spectroscopic data available on rings in the scatterfree, few electrons limit in which quantum effects are best manifested. Previous spectroscopic studies dealt with microscopic rings 3 in GaAs-Ga x Al 1Ϫx As heterostructures, fairly well reproduced by classical or hydrodynamical models. 4,5 In spite of the lacking of experimental information, the study of nanoscopic ring structures has already attracted a strong theoretical interest. [6][7][8][9][10][11] We recall that due to the nonapplicability of the generalized Kohn theorem, a very rich spectroscopic structure is expected to appear in few electrons nanorings, as anticipated by Halonen, Pietiläinen, and Chakraborty 9 and also found in recent works. 12,13In this paper we attempt a quantitative description of some spectroscopic and ground-state (gs) properties of the experimentally studied nanoscopic rings 1,2 using currentdensity ͑CDFT͒ and time-dependent local-spin-density ͑TDLSDFT͒ functional theories. The reason for such an attempt is twofold: on the one hand, to contribute to put on a firm basis the interpretation of current experiments as manifestation of actual properties of few-electrons ring-shaped nanostructures; on the other hand, although in principle exact results could be obtained for one and two electron rings using, e.g., exact-diagonalization methods, 8,9 the present one can also be applied to many electron systems, 12 and we think it is worthwhile to explore the capabilities and limitations of density-functional methods to describe such small rings.Following Ref. 6, we have modeled the ring confining potential by a parabola,with 2 R 0 ϭ 14 nm and the frequency 0 fixed to reproduce the high-energy peak found in the far-infrared ͑FIR͒ transmission spectrum at Bϭ0. For Nϭ2 electrons this yields 0 ϳ12.3 meV. The electron effective mass m*ϭ0.063 ͑we write mϭm*m e with m e being the physical electron mass͒ and effective gyromagnetic factor g*ϭϪ0.43 have been taken from the experiments, [14][15][16] and the value of the dielectric constant has been taken to be ⑀ϭ12.4.To obtain the structure of the GS we have resorted to CDFT as described in Refs. 17 and 18, and to obtain the FIR absorption we...

Energy spectra and oscillatory magnetization of two-electron self-assembledInxGa1−xAsquantum rings in GaAs

“…A quantitative determination of the Wigner crystallization onset for the two electrons in a parabolic two-dimensional confinement has been provided. 22 The far-infrared transmission spectrum of InAs self-assembled nanoscopic rings obtained using the timedependent local-spin-density theory 23 is in agreement with the experiment. 7 On the other hand, numerical methods were extensively used, which allow for the investigation of advanced confinement models.…”

Multipole modes and spin features in the Raman spectrum of nanoscopic quantum rings

“…These values are close to the ones used 21 to describe the rings studied by Lorke et al 3 The electron effective mass m*ϭ0.063 ͑we write m ϭm*m e with m e being the physical electron mass͒ and effective gyromagnetic factor g*ϭϪ0.43 have been taken from the experiments, [32][33][34] and the value of the dielectric constant has been taken to be ⑀ϭ12.4. The model is strictly two-dimensional, and as a consequence of circular symmetry, the single particle ͑s.p.͒ wave functions are eigenstates of the orbital angular momentum l z and can be written as u nl (r) Figure 1 shows the addition energies ⌬ 2 (N) at zero magnetic field.…”

“…11 as a consequence of Hund's first rule which favors the occurence of ferromagnetic S z ϭ1 phases. A ring with a low degree of one dimensionality tends to lose the periodic features of the ideal ring wire, being somehow an intermediate case between a ring wire and a quantum dot, and for these systems the effect is not so marked, 21 appearing as a small amplitude oscillation whose B width coincides with that of the ferromagnetic phase ͑see Fig. 3͒.…”

“…These AB oscillations have been observed in mesoscopic rings in a GaAlAs/GaAs heterostructure by measuring the conductance across the ring. 20 The experimental results for one-and two-electron nanoscopic rings have been theoretically analyzed 21 using the current density ͑CDFT͒ and time-dependent local-spin densityfunctional ͑TDLSDFT͒ theories, and a good agreement between theory and experiment is found ͑see also Refs. 16 and 19͒.…”

Magneto-optics of layers of semiconductor quantum dots and nano-rings

“…Far-infrared spectroscopy enabled the investigation of transitions between the split levels directly and revealed level crossings for the rings with varying magnetic field, unknown from dots [10]. MP spectroscopy has been used to demonstrate neutral and charged excitons in nano-rings [8].…”